Independent of capped convertible notes being problematic under some assumptions (essentially, when the market turns down and you raise at less than the cap -- that's 90% of the problem, and 9% of the rest is when you don't then sell for enough to blow the pref out of consideration), an investor trying to lowball you on the cap is no different from lowballing on equity valuation.
If everyone is investing at $12mm, and an investor says "fine, but I'm special, give me $6mm or I won't invest", there's no difference if it's capped convertible note or equity (except that it's technically more difficult to do the investment as equity with different valuations; you can hack it by giving warrants or other benefits I think.)
If everyone is investing at $12mm, and an investor says "fine, but I'm special, give me $6mm or I won't invest", there's no difference if it's capped convertible note or equity (except that it's technically more difficult to do the investment as equity with different valuations; you can hack it by giving warrants or other benefits I think.)