Nope not yet. I bet Koodo will start offering LTE with the launch of the iPhone 5.
Virgin Mobile has went LTE so I'm surprised that Fido and Koodo haven't followed suit (unless Fido started offering LTE very recently. I haven't exactly been following MobileSyrup and HoFo much recently).
IMHO, Koodo has the overall better plans compared to Virgin Mobile. But if you want LTE and plans similar to Koodo's, Virgin is worth a look. Their $35 Incoming and myBuddies 10 plans are really, really good (especially the myBuddies 10 one if the myBuddies is more beneficial to you than unlimited incoming) and set them apart from Koodo. Though Koodo does have an unlimited incoming Canada-wide plan that offers 50 more daytime minutes but it starts at $40, not $35.
Some people have said that Virgin is just as good as Koodo now. But I disagree. I have the City Koodo Unlimited (Virgin has the exact same City Unlimited plan) paired with the $2 long-distance saver (which gives you 5c/min Canadian long distance) and $15/500 MB data connect. Virgin does not have a Canadian long-distance saver or a $15/500 MB data add-on. For my personal needs, Koodo is better. But Virgin's $35 Canada-wide Unlimited Incoming or myBuddies 10 will benefit a lot of people.