Shyv can not turn invisible to bypass wards (or force the enemy to spend twice the amount of gold on more + more expensive wards since they'd have to ward both approach and the lane itself.
This is assuming that the enemy team will mass-buy pink wards, and not just rape you and set you behind the first time you pass one. People are warding anyway, supports will usually pink ward bot anyway, and it's not uncommon for top to do so too.
Once shyvana is in position in a gank, she does roughly the same damage as twitch, unless the enemy jukes around minions (twitch is ranged and less vulnerable to bad pathfinding) or flashes away (where twitch can still expunge). Although twitches early damage (lv 2-4ish, especially level 2) is vastly higher than shyvs due to attack speed steroid and expunge
This is the only valid point I've seen so far. Valid in the sense of comparing Shyv to Twitch. However, Shaco does everything Twitch does 2-4 better. (Except force someone to buy 1 pink maybe, range is not a concern cause of Shaco Q - oh and Twitch is better at scouting, no idea why you'd not just ward at 2-4 though)
Twitch can more reliably show up between the enemy and their tower, forcing them to move past him, whereas shyvana will often find herself catching up to enemies.
I'm assuming you're not talking about mid here, since there's barely space for Twitch behind mids tower and where he should be, except he's going fully aggresive or something, in which case, any jungler could show up behind him. For top, you could potentially show up behind the enemy early levels, if they're pushing (which most good tops will try to early on, in most situations - except when expecting lvl 2 gank or if SOMEONE on the other team has the ability to go invisible). After lvl 6, top, Twitch can be expected to be lvl 4ish. If a lvl 4 Twitch is willing to move in between top tower and a lvl 6 Vlad, Shyv, Garen, Lee Sin, he's got some balls. The level difference only scales in tops' favor from this point on.
I guess this leaves bot the most likely option for a kill (considering decent plays, mistakes do happen, but this applies to both lanes as well as the jungling Twitch). Bot also happens to be the most warded lane, and the most passive one usually, and first blood on bot lane are statistically proven to have little to no effect on game outcome. (My personal theory is that this is due to the passive play)
So compared to shyvana in the laning phase, twitch has better initiation/gapclosing (especially before top/mid have had their first bluepill), better stickiness and higher damage output. This equates a better ganking kit, a higher chance of getting kills during ganks and therefore a bigger likelyhood of getting fed.
In retrospect, Shyvana was a pretty horrid example, as she isn't a strong early ganker at all. But Twitch could be replaced by Shaco and make this whole paragraph more true.
In games where I farm instead I have boots + wriggles + 1x dorans + IE at the 24-25 minute mark.
In order for this to be true you'd have to have aqcuired 6825 gold by this point. You will have gained 1800ish gold passively as well as 475 to start with, so that leaves 4550 gold that you would have to get from minions or monsters. Jungle is worth less than lane in terms of gold, but to make it easier, I'm gonna use lane minions for reference (which is on average 22~ gold per minion, this is maybe even on the high side, since it's this early in the game). In order to get 4550 gold from minions you would have to have 206 CS at this point. I doubt it. Subtract 14 CS for each kill you have.
Also I can't help but comment that you're currently 3-8 in ranked with Twitch. I remember you as a decent to good player, so I assume this winrate is due to a champion problem and not personal skill.