Obviously, the Leyline is better than the Witchbane Orb, as it can come into play for free if it's in your opening hand. The Orb is an artifact that costs 4 to cast, although it does have the upside of destroy any Curses in play (and Curse of Death's Hold has seen some Modern play.) But really, you're not going to spend a whole turn casting the Orb, are you?
There's also a similar card that used to see play in Legacy. It's a card originally printed in Onslaught called True Believer, but later reprinted in 10th Edition which made it legal in Modern. It's a 2/2 for WW instead of a 2/1 for 1W. But the major difference is that it gives you shroud, which means you can't even target yourself. This can actually prove to be a downside, since there are many cards that can benefit you by targeting yourself. So, in Aegis of the Gods VS True Believer, the Aegis wins overall.
There seemed to be plenty of good reasons to play Aegis of the Gods in Standard. But, besides the typical burn decks, it wasn't clear how good it would be in the Standard format of the day. One major rules question at the time was how Aegis of the Gods interacted with the powerful God, Athreos, God of Passage's ability. Gaining hexproof does in fact stop Athreos players from returning their own creatures to their hands. It would turn out to be a corner case, but still relevant.
Alternatively, giving yourself hexproof didn't stop the Tribute mechanic featured in Born of the Gods, since it didn't target. But that ability turned out to be rarely relevant in competitive play anyway. It also doesn't stop Extort, which was a major mechanic in Gatecrash, since that doesn't target, either. Basically, most the things that people wanted it to stop, having hexproof doesn't solve.
(Side note: There was also a question at the time about if Aegis of the Gods would be an issue for your teammate in the then quite popular Two-Headed Giant format. The good news is that even if you have hexproof, your teammate can still target you, since hexproof only affects opponents. So yes, Aegis of the Gods is good in Two-Headed Giant, for whoever still plays that format. It's fun and more people still should!)
All in all, Aegis of the Gods is a decent card with a very relevant ability. But it turned into more of a sideboard option, and not even in Standard. Competitively, the Aegis of the Gods has found permanent homes in the sideboards of Vintage decks, and not just Death and Taxes, white weenie, or Hatebear decks. So many Vintage decks win with effects that get shut off by you having hexproof.
Why does it work so well in Vintage and not in other 60-card formats? The main issue is how fragile a 2/1 really is. It's far too easy to remove in Modern or Legacy. But in Vintage, having to use a removal spell on him is going to be a lot more important than in any other format. Decks in Vintage are all about executing their game plan. Even if the Aegis just buys you a turn to "go off" it's done its job. Basically, in Vintage, it's at the very least a pest. Sometimes, you only need that one pest to give you the edge. Currently, the best deck that uses Aegis of the Gods is White Eldrazi.
In EDH / Commander, Aegis of the Gods sees a fair amount of play. Unsurprisingly, it's most used in Daxos the Returned decks, which uses every good low-cost Enchantment available. But it also sees play alongside Zur the Enchanter, who can tutor it straight from the deck into play, which is a pretty powerful move. It sees a smattering of play across a great many other decks, as well.
How much is Aegis of the Gods worth? As it's not a staple in any particular deck, Aegis of the Gods' price has been around $2 for quite some time. The Aegis's foil price, however is closer to $4. The foil is definitely a good investment if you plan on playing a copy in Vintage or Commander.
If you're looking for a budget alternative to Leyline of Sanctity, though, Aegis of the Gods is probably a bit too fragile to play in most formats. It's good in Vintage and Commander. But, if you're looking for a good answer to giving yourself hexproof in Modern or Legacy, I'd stick to the Leyline.