Maxi biggest advantage is his biggest disadvantage, he is the better close combat fighter and has higher AP, but his mind manipulation is very minor and he gets outrange.
Claude only really needs to hit with Encloser once to actually secure the victory via stalling and outrange and that's actually very often to happen due skills such as Bow Prowess Lv3 and his Stats Amp, which reduces the AP gap of 999.8 kilotons and 650 kilotons while making him faster.
Could Claude get into a close combat fight? Why he would in the first place, he's very smart in the battlefield and Maxi fits the brawling class type to a T, which is very got a close combat. Maxi is not dumb in any means, but Claude is just the smarter fighter. Even in a close combat, he is not hopeless since at best, his evasion ring makes him capable to escape the attack and counterattack and he could even take some hits in other situations.
Maxi would win in his best scenario due being just more skilled and stronger, but Claude wincon is just more frequent. Voting for Claude.
I checked again Maxi and Claude pages so, the changes in AP are still in Maxi's side with 92.2225 Megatons of TNT against Claude's 85.45 Megatons of TNT, but it makes the gap much closer (1.08 to be exact).
Now, Maxi is now much more experimented than a Academy Arc Claude and has an extended attack in fire manipulation, so he will have a better chance at getting his opponent into a close combat.
That being said, my reasoning in Claude's victory remains due Encloser let him stall and outrange him, while Stats Amp would probably tie the AP gap.