Aren't they about the same? I was wondering if it was worth my CE to make a Levi when level 10 does quite a bit of damage.
Ascended Calibur (Level 10) vs. Basic Levi
A fully heated Acended Calibur will actually even outperform a freshly crafted Levi. After the Levi is heated fully it will however produce slightly more damage. The Levi is a largely cosmetic upgrade that I would recommend putting off in favor of upgrading other gear. I would for example value an Elite Slash Module over upgrading an AscCal to Levi. I ran an AscCal with gear to put it at DMG+ Very High and it outperformed most of the Levi users that I was playing with at the time. Once you get into specialized damage types though, you will likely not use a Levi very much at all (mine pretty much only comes out for Vana's mask).
*edit* Most of the time I would agree with Malsvir-Branea's comment about 4* vs 5*, however, in the case of Ascended Calibur vs Levi the damage advantage of the Levi is very slight & it was painful for me to pay that much CE & CR to nerf my blade (until heated when it does slightly more).
Also, note that the Levi has the exact same reach as the other Caliburs even though the model is waaaaaay bigger.
On the wiki, you can find damage numbers for Levi and Asc. Calibur at heat level 10. These are the only numbers that really matter; after all, your Levi would be at heat level 1 for an extremely short time, right?
If you really do want to know about the difference between heat level 1 and heat level 10, we've collected a little data (on BTB) at http://forums.spiralknights.com/en/node/50679. The damage output seems to increase by roughly 30%.
They do about the same damage, but the Levi will still gain damage as it levels up toward 10. There is no reason in this game to prefer a 4* piece of gear over a 5* piece of gear, provided both pieces are from the same alchemy paths.