The best answer anyone will be able to give you is 'maybe', as it will depend a lot on the exact situations - and in particular the reason that your visa was refused.
The US is often relatively strict when it comes to giving B1/B2 visas to people from VWP-eligible countries, and generally will require them to provide a suitable reason why they would not be able to enter the country under the Visa Waiver Program and thus require a visa to be issued. If you do not have a suitable reason for a visa then you will be found ineligible under section 214(b).
Section 214(b) will also be used if the consular staff believe that you were likely to stay in the US longer than you were allowed, planning/likely to work whilst in the US, or
likely to break any of the other conditions of the visa. With the information you've given it's not possible to know which of these reasons caused the rejection.
Your best option at this stage is to apply for an ESTA, and CORRECTLY answer the question about having been refused a visa. Based on the actual reason for your visa refusal, your ESTA may or may not be approved. You may find that your ESTA takes longer than normal to be approved/rejected, as it will likely need to be manually processed.
If your ESTA is refused then you have no option but to re-attempt applying for a visa, or give up on your plans to visit the US at this time.
If your ESTA is approved then it's likely you will have no problems when entering the US, although it is possible that the immigration staff will ask you some additional questions based on the reason for your prior refusal. Again, this will depend on the exact reason for your visa refusal, and any notes that the consular staff made on your record about that refusal.