Will you ask your site competitor's member to join your site by sending message to them through competitor's site (like maybe sending message,mail etc)?
Do you think members who received such an invitation will get annoyed even the promoted website is in someway better?
Poaching users is almost always frowned upon (both by businesses and users being poached). Possibly Illegal too (though IANAL)
However within reason you are allowed to "present" an offer or market the PROs of your service over theirs.
I think however using the competitor's system, to send bulk email solicitations to their users to try and sell them on jumping ship... certainly crosses some questionably ethical lines.
I think I would lean towards finding a 3rd party forum where you can post as a rep of your company (or sneakily as just some random user ) either questioning the differences between the two services... or posting your "observations" as to why you feel "B" is better than "A".
If you do this in an informative way... without slandering your competitor I think you'll be able to provide "info" to those that may be on the fence... or looking to switch.
 Be careful if doing this... its a very gray area... be gentle and provide quality information... if you post "hate/lies/rumors/etc." if/when it gets traced back to you it could really hurt your reputation.