Saim-Hann is wilder, fiercer. Ulthwe on the other hand is slower, considering all options. Don't think about bikes or any troop types, it's a mindset question not a "hardware" question.
Altansar because they're the home of the Dark Reapers and because Phoenix Lord Maugan Ra is a total badass.
Bear in mind, prideful to a fault is something which has been brought up with factions in the past, without it being utterly detrimental. It doesn't need to be taken to "They can never be Ultramarines" levels, but perhaps to levels seen with the likes of the Dark Eldar, or White Scars. It encourages them to pull off even more insane stunts than usual, push their abilities to the limit to prove they have earned their reputation and remain self-assured enough to attempt things no sane eldar would. Plus, of course, the eldar think and act on a different level from humans so it might resonate with them in a different way than it would humans. It's just that it sometimes takes them into situations where they cannot hope to actually win certain battles. Please understand, i'm not saying one is better than the other, but Saim-Hann is still most certainly worth a look despite that small note there.
Your options. The tricky and cunning. The badass and unrelenting. It is obvious that you should pick Lyanden.
Ulthwé and Saim-Hann are my two choices for an eldar character's craftworld since there is no Alaitoc, so I thought to give some kind of an opinion here, as an eldar. Except that I will not give it as an eldar, because... RED UNZ GO FASTAH
I find that pride and honor tend to go hand in hand. Examples include both the Lion and Crane clans of L5R/Rokugan (really, samurai in general), crusaders/knights, most of the generals of the Romance of the 3 Kingdoms (I don't remember what the time period is actually called), etc. I'd recommend Saim-Hann based on what you said you are looking for, but I'm not sure what you have against pride, which could be the deciding factor. There's also a hair's difference between healthy confidence and pride. I'm rolling Altansar as my main. Saim-Hann would be my next choice.
Pride is one of the easiest traits to corrupt. Pride can lead to arrogance. Someone that becomes too prideful will believe they are better than everyone. Too much pride leads to Chaos.
It helps when you are better than everyone else On a more serious note, I'm not an expert on Eldar lore, but I think that either they can't be corrupted by Chaos at this point in time or the Chaos gods just don't care to, because there isn't a Chaos Eldar faction. If someone is prideful/arrogant, it's usually because they've succeeded often enough for that opinion/mentality to be valid (until proven wrong). Even then, it's part of the reason that they accomplish more than someone that is overly humble, because they will dare to achieve more. Killbo used stunts as an example. One of my friends has always been very prideful/arrogant. I made fun of him for it at first to try and bring him back to reality (High school is a silly place), but I realized over time that it actually has a positive effect on both him and the people he is around. Despite that, the text does say "to a fault", so we have to assume something is bad about it. However, the only example that they give is fighting with other Eldar over issues of honor. That sort of sounds like Klingons in Star Trek to me. (But how many factions in 40k would really let another faction get away with insulting their honor without violence?) TL;DR If you like Klingon pride & honor mentality then you will like Saim-Hann.
