Now, about his mobile suit... by most it seems people consider his or Quatre's mobile suits to be the most useless. I can understand that. Heavy Arms runs out of ammo quickly. Heavy Arms carries the most firepower of any of the suits. To some extent one might say he is the only one that uses bullets. Once they are gone, all he had left is a knife that rather comes out of the right arm like a Swiss Army blade. Still it is made of Gundanium and on the times he fall back on it, he puts it to good use.
Nevertheless, the Gundam he pilots seems to work fine with his style of fighting. He is mainly a strategist and is an infiltrator most of the time. He can fight, but he seems best at doing things without the Mobile Suit. When working as a spy in enemy lines, he is pretty much perfect at acting. When he worked as a member of OZ, Wu Fei was even tricked by his abilities. When he finds out what Trowa managed to smuggle to them from Master O, however, Wu Fei is clearly impressed. Trowa also can pilot or drive any sort of transport machinery with ease. With the addition of being able to repair, he can certainly go behind lines and disembowel or reprogram enemies' suits.
Trowa makes up for any down faults to the Gundam. As a Gundam Pilot, he is not afraid to die and thus he fights with a potential that only he and the four other pilots posses, giving him an advantage over his foes. He uses his strategic skills and when there is nothing else left, he will simply surrender. That usually works to his advantage because it takes him either into his enemy's base or he could possibly take them out if the number is one he can go against.
Even more, the Gundams were not created by the Pilots. They were designed by the scientists and then had a person picked to pilot it. In the end, as shown in the final episodes of the television series, the Gundam Suits were really made as components to make a whole as a fighting force.
In addition, the Gundam Heavy Arms was originally made for the real Trowa Barton of the Barton Foundation. The man is described as headstrong, brash, aggressive, and immature by producers of the show, which pretty much is the exact opposite of the Trowa Barton once known as Nanashi.
Recklessness would be expected from someone like that and firepower would suit his personality just fine. The colors of Heavy Arms were flashy also, which suits Trowa Barton of the foundation rather than Trowa Barton the pilot. I'd say the real Trowa Barton's manner of handling things simply would have gotten him killed in the very beginning.
Despite that, the Trowa who does become Pilot: 03 is skilled. It is the pilot that ultimately decides the battle. If anything, Trowa is an expert with mobile suits.
In "Episode 16: The Sorrowful Battle", he easily takes up Wing Gundam and uses it to fight off a search party so Heero and Zechs can fight. As seen in the episode before it, Trowa had to teach Heero how to function Gundam Heavy Arms.
It was already a given that in "Episode 20: Lunar Base Infiltration" that he'd be amazing at displaying the abilities of a Taurus and later as the Vayeate was created he was selected to pilot it first and he used it well.
In "Episode 21: Grief-Stricken Quatre", he and Heero test the suits against the Tallgeese. While fighting Zechs, who now goes by his birth name Millardo Peacecraft, they strategically get rid of the surrounding Taurus suits around them as well.
Later in "Episode 24: The Gundam They Call Zero" when they meet up to see the Gundam Zero, Trowa doesn't see Quatre as a threat to him. With that fact, he still manages to dodge while the other OZ suits around him are obliterated.
Despite his amnesia in "Episode 38: The Birth of Queen Relena", Trowa steals a shuttle and pilots it easily as he heads into space. Some might say he already knew how to do such, but it isn't like Trowa remembered what he could do as a pilot. It was only until he got the feel down did his body likely remember.
In "Episode 39: Trowa's Return to the Battlefield" he is the first to set out when attacked by OZ, who believe they are members of White Fang. He easily takes up a Taurus and heads out. He is still undeniably strong even though he is half winging it and half remembering how to pilot a Mobile Suit. His reflexes are still superb as he dodges the multiple OZ Taurus Suits and demolishes them with assumable ease.
He has proven to be an efficient and presumably "perfect soldier". He may not have received training like Heero Yuy to pilot Heavy Arms, but unlike the real Trowa Barton, he had experience in fighting from since he could remember instilled into him no matter what.
Even with his memories still missing Trowa gives hint to his abilities to assess situations and where strengths and weaknesses lie as he is out with Quatre, Duo and Noin in "Episode 41: Crossfire At Barge". He knows he is not as capable a fighter with the state he is in, but does what he can. Quatre and Duo will most certainly be able to protect and aid Noin as she tries to get to Zechs. Thus, Trowa quickly decides to protect the civilian Colony nearby so he will not cause worry or troubles to the others should he falter.
When the Colony is hit by the Barge's cannon, he goes to aid the others. He managed to save Noin upon arrival and started to fight of OZ Taurus Suits.
In "Episode 43: Target: Earth", Trowa still has amnesia. That doesn't stop him from stealing Wing Zero when he sees Catherine is in danger. He easily starts it up and heads off into space in flight mode. He's got the Gundam down even though he never used it before.
He uses Wing Zero and like the other pilots, hallucinates under its influence. All the while he tries to keep his focus. Quatre manages to snap him out of it and in turn he gets his memories back. By speculation, the ZERO System showed him his future by showing him his past... It showed him the three people he wished to protect.
Thus, in the end, Heavy Arms may not seem like an amazing Gundam to some, but it doesn't matter. What matters is how you use what you are given and that use it to its greatest potential.