After researching and reading a bunch of material and reviews, here is my conclusion of most favorite services out there.
Moniker.com - Moniker sounds to be the safest escrow service for buying/selling domains. What makes them different from anyone else is that they first require the domain name to be moved to their own registrar. This alone puts them in complete control of the transaction and ensures that it will go without a buyer either changing his/her mind half-way (or, most commonly, not confirming the transfer after the domain is pushed, which in most cases can delay the resolution for seller for upto 60 days or more) or just intentionally trying to scam the seller
Escrow.com - the most popular service due to its name, years in service, mid-range cost. PayPal funded transactions are limited to $5,000. Escrow does not control the domain names being sold, but they still remain to be the most trusted and most commonly used service.
Transpact.com - less known, U.K-based, but also the most affordable escrow service around that has gained enough positive feedback in recent years. Transpact has fixed costs and offers a possibility to execute transaction in various currencies. It has a limited number of countries they are working with. The advantage is clearly the cost. The disadvantage is that due to government policies you have to submit more private information than with other services.
Transpact is the service I will likely use in my upcoming domain name purchase. While Escrow charges at least $162, Transpact will cost around $50 for the same transaction. Regardless of service I end up using, I will try to share my feedback here after.