A customs union is more than free trade (o.m.'s answer). It's about e.g. having a set of standards for imported products. If (say) you can import chlorinated chicken in the Eurasian Union, but you can't in the European one, what is a country member of both going to do without breaking either treaty, etc.
Or as former deputy chairman of the Russian Central Bank explained in a 2014 article:
This point calls for a technical explanation: countries rely on several forms of bilateral and multilateral agreements to facilitate foreign trade. The two most common are Free Trade Areas (FTAs) and Customs Unions (CUs). In an FTA member-states agree to eliminate all (or the bulk) of tariffs on each other, but maintain individual tariff policies vis-a-vis third parties. Thus, when countries join an FTA, they do not commit to cooperate with each other in setting their import tariffs. A CU is a closer and more sophisticated form of international cooperation whose main feature is the establishment of the supra-national authority to which the members of the CU delegate their power to decide upon joint import tariff regime (including rates). CU members are not allowed to join another as it may lead to regulatory conflicts.
In 2007, Russia, Belarus, and Kazakhstan have agreed to establish a EACU that came into existence in 2010. The tariff policy within the EACU was delegated to the supra-national agency (initially Commission of the CU, since July 2012—Eurasian Economic Commission). As a result, Russia, Belarus, and Kazakhstan are not able to change their tariff rates alone but need to coordinate steps with two other members of the EACU. The EACU Treaty also prohibits its members to join other CUs.
And besides those, various other concerns have been raised, on the Russian side:
According to President Putin, he warned former President of Ukraine Viktor Yanukovych about the problem of European goods flooding the Russian market through the free trade arrangement with Ukraine when they discussed this issue in November 2013, on the eve of the Vilnius Summit, where the signing of the AA and DCFTA was set to take place. However, Prime Minister Medvedev was ambiguous in his statement on this issue and said only that the impact of Ukraine’s signing an AA and DCFTA was uncertain.
Expanding on Putin’s grim forecast, Russian chief negotiator in the World Trade Organization Maksim Medvedkov, has focused on a possible threat to the Russian economy as a “domino effect,” whereby Ukrainian goods will be driven out of Ukraine by European ones and will instead be sent to Russia. Alternatively, the territory of Ukraine will be used by EU companies for simple operations in finishing, assembling, and then re-exporting their products to the Customs Union.”
Other Russian leaders have sounded more dire predictions about the impact of the AA and DCFTA signing on Russian interests. Deputy Prime Minister Dmitri Rogozin has stated that “an [AA] with the EU is a change in the neutral status of Moldova. There is a certain rule that all NATO members know: in order to enter the EU, you are required to join NATO. This rule will not change for Moldova. All countries go through this. Therefore, association with the EU will be the moment when Moldova turns the doorknob of NATO.” This statement, despite it being false, appears to reflect the real concerns of Putin personally and is one of the main drivers of Russian policy.
Ulyukayev’s deputy in charge of international economic cooperation Andrei Likhachev, was also quite subdued in his comments. He focused on the possible conflict of regulatory norms in the future:
“Moldova will not be able to combine two regulatory systems: the CIS and the EU. It will be forced to make a certain choice. And if that choice will be in favor of the European system, then the CIS system will cease to be comfortable. … If Moldova signs the agreement with the EU, it may encounter contradictory obligations in customs and transport regulations, sanitary and migration control. Moreover, the most painful issue may turn out to be the differences in the application of sanitary norms and migration policy.”
The last one is actually a reiteration of my initial point.
The EU's position is less detailed in that article, but paraphrased as:
The DCFTA in its current form does not allow any of three countries to join Russia-sponsored EACU because in such a case EU should start FTA negotiations with the entire CU, while the EU is not ready for that;
DCFTA - Deep and Comprehensive Free Trade Area
AA - Association Agreement
EACU - Eurasian_Customs_Union