Originally Posted by Dany
They're both correct.
The verb "appear" is stronger than "seem". To me, a speaker who uses the sentence with "appears" is more confident the offer could be competitive. He/she probably bases this statement on more concrete ideas and knowledge. The verb "seem" indicates an idea that is based on something less concrete in my opinion.
He seems to be happy. -- That sounds kind of iffy to me.
He appears to be happy. -- That sounds more confident to me.
That's how I explain the difference between "appear" and "seem". They are listed as synonyms, but I don't hear or understand them as being quite exactly the same.
Student or Learner