Franky
Love: He's fun and funny. He's a self-patched together cyborg powered by cola. What more need I say? His story during Water 7 was pretty powerful, and a real highlight in the series. His fighting style is all guns & metal, very much unlike the other Strawhats, and he carries it in a fun way. I love how in Thriller Bark, he brought some nunchuks … which he could make bigger using broken pieces of pillar! And those anti-monster bullets or whatever which he had over his shoulder for the whole arc before finally using them on Oars. He made that mega hose to wet Oars (or something like that). And he randomly built a bridge (and stairs that kind of fell away behind them, but let's not think about that). He's wild a crazy and gets emotionally touched by every damn sob story, and despite that is somehow always unfazed against pretty much any odds (this happens more post-timeskip). And Coup de Vent is one of the best attacks in the series. His three litre fuel limitation is pretty significant, and particularly made for a fun battle against Fukuro. In general, the fact that he used half his fuel to use a full power Coup de Vent made it costly, which is something the other characters don't much have (except Chopper).
Loathe: Post-timeskip, Franky just ... doesn't do much. He's just there. I don't mind his new design - some of his new hair has been annoying, but otherwise I'm mostly okay with it. That said, I'm not feeling the beam. It was nice to see Coup de Vent is still around as a lesser attack, and that the land version Gaon Cannon - another air cannon attack - is his best attack. And the tank is cool. But ... where's the fuel limitation?? It's really disappointing to me that he doesn't have that anymore. And then there's the fact that, unlike in Thriller Bark, he hasn't bothered making anything mid-arc or using some random extra weapon in an arc anymore. And, the Bracchio tank and Rhino bike were kind of cool (will they even appear again?) but General Franky was a half-funny gag that afterwards is basically just some lame thing Franky sometimes uses. It's boring. So he can sit in some big, silly looking robot that does nothing. He can shoot beams like the Pacifistas. He can cause tired gags about robots being cool with some boring tired sexism thrown in. Where's the fun and unique Franky of old? What happened to him? Maybe it's just the arcs are more crowded and rapid these days, and that we only had one arc pre-timeskip where he wasn't in the spotlight anyway, but I've been really disappointed with post-timeskip thus far.
edit:
More simply, it's like Franky's become some mecha with little aesthetic nice things, robot style weapons (beam ...) and a dumb non-contributory super-mecha to sit inside. Before, Franky was physically rough-and-ready - a metal brawler with guns stuffed in here and there, included an air cannon, all of which drained away his precious fuel. Needs more punching, more improvised craft and temporary weapons and more FUN.
4.5/5 - recent arcs have really let him down, and I'm mostly giving him such a high score both in memory of how great he was in Water 7 and Thriller Bark and in hope for what might come even in Dressrosa.
Franky's had one serious fight post timeskip that we've really seen anything of.
That fight was inside the General Franky.
Franky will still be a brawler and have the stuff we loved him using pre-timeskip, just give it time.
He's had a fairly prominent role in Dressrosa as the one to be in contact with the toy soldier, planning Luffy's entry into the tournament, and now attempting to sack the Toy House. In the last arc he was gone for a lot of the time away but even with that extended absence he still swapped bodies with Chopper, unleashed Monster Point, had his own body sought after by Caesar and then took down 2 members of the Donquixote family single-handedly and without breaking a sweat. So I don't really get how you can claim that post-timeskip he just stands in the background.
Also, it's pretty reasonable for him to not have the fuel limit anymore. All the SH's have moved on over the 2 years and if Franky hadn't been able to address one of his major weaknesses during the 2 years he spent in the secret lab of a man 500 years ahead of his time then tbh I'd be pretty damn disappointed.
Franky is as good a character as ever, he still has all his fantastic mannerisms that you mentioned (Ok, post-timeskip he hasn't randomly built something yet. No situation has really called for it though.) and even more with his interchangeable new design.
Franky is a 5/5 without a shadow of a doubt.