Bakelite resin is a phenol formaldehyde resin formed by condensation reaction of phenol or substituted phenol with formaldehyde. Epoxy resin is a low molecular weight pre-polymer or higher molecular weight polymer which normally contains at least two epoxide groups. The epoxide group is also sometimes referred to as a glycidyl or oxirane group. They may be reacted either with themselves through catalytic homopolymerisation or with a wide range of co-reactants including polyfunctional amines, acids (and acid anhydrides), phenols, alcohols and thiols.
They both are thermosetting polymers, but Bakelite resin has been replaced by epoxy resin in recent times with more reinforcement features embedded in them.
More on phenolic resins can be found in the 'Phenolic Resins: Chemistry', Applications, Standardization, Safety and Ecology by A. Gardziella, L.A. Pilato, A. Knop, 2nd edition, Springer, 2000
Reinforcement effect of epoxy resin under fully cured condition is higher than Bakelite resin; both in terms of stiffness gain and flexural strength gain could be higher if epoxy is being rightly coupled with reinforcement component.
For high temperature resistance, Bakelite is preferred. Both Bakelite and Epoxy are used as matrices and both are brittle. In order to increase the strength, both are to be reinforced. Compared to the tensile strength of the matrices, epoxy has higher value than Bakelite.