What are the similarities and differences between the lanthanides series and the actinide series?

Mainly, the actinides have bigger orbitals, but their #5f# orbitals are more radially compact compared to the #4f# orbitals of the lanthanides, so there are more so-called "Aufbau exceptions" among the actinides.

Other factors are listed below, like electronegativities and oxidation states.

Here it is in a table... #"L""n"# #=# #"lanthanide"#, #"An"# #=# #"actinide"#.

#" "" "" "ul(" "" "" ""Electroneg."" ""Atomic Radius"" "" ""Oxid. States"" ""Exceptions")#
#"L""n"color(white)(..........)"Lower"" "" "" "" ""Smaller"" "" "" "" ""+3 usually"" "" "3#
#"An"color(white)(.........)"Variable"" "" "" ""Larger"" "" "" "" "color(white)(.)"+3 to +7"" "" "" "6#

• The electronegativities of the lanthanides are lower than for the actinides, but also more consistent. The actinide electronegativities are quite diverse. This is a graph made from data in Tro:

• The atomic radii of the actinides is bigger simply due to a new quantum level as expected.

• The actinides also achieve more diverse oxidation states due to higher #d# orbital participation. Thus, their oxidation states range from #+3# to #+7#. The #+3# oxidation state is somewhat common among them, but less so than among the lanthanides.

Lanthanides:

Actinides:

• Lastly, there are more electron configuration exceptions among the actinides, due to that higher #6d# participation.

The exceptions are #"La"#, #"Ce"#, and #"Gd"# for the lanthanides, and #"Ac"#, #"Th"#, #"Pa"#, #"U"#, #"Np"#, and #"Cm"# for the actinides. In red are the exceptions.

#color(white)([(color(red)(La),(color(red)([Xe] 6s^2 5d^1)),color(black)(Tb),(color(black)([Xe] 6s^2 4f^9))),(color(red)(Ce),(color(red)([Xe] 6s^2 4f^1 5d^1)),color(black)(Dy),(color(black)([Xe] 6s^2 4f^10))),(color(black)(Pr),(color(black)([Xe] 6s^2 4f^3)),color(black)(Ho),(color(black)([Xe] 6s^2 4f^11))),(color(black)(Nd),(color(black)([Xe] 6s^2 4f^4)),color(black)(Er),(color(black)([Xe] 6s^2 4f^12))),(color(black)(Pm),(color(black)([Xe] 6s^2 4f^5)),color(black)(Tm),(color(black)([Xe] 6s^2 4f^13))),(color(black)(Sm),(color(black)([Xe] 6s^2 4f^6)),color(black)(Yb),(color(black)([Xe] 6s^2 4f^14))),(color(black)(Eu),(color(black)([Xe] 6s^2 4f^7)),color(black)(Lu),(color(black)([Xe] 6s^2 4f^14 5d^1))),(color(red)(Gd),(color(red)([Xe] 6s^2 4f^7 5d^1)),"","")])#

#color(white)([(color(red)(Ac),(color(red)([Rn] 7s^2 6d^1)),color(black)(Bk),(color(black)([Rn] 7s^2 5f^9))),(color(red)(Th),(color(red)([Rn] 7s^2 6d^2)),color(black)(Cf),(color(black)([Rn] 7s^2 5f^10))),(color(red)(Pa),(color(red)([Rn] 7s^2 5f^2 6d^1)),color(black)(Es),(color(black)([Rn] 7s^2 5f^11))),(color(red)(U),(color(red)([Rn] 7s^2 5f^3 6d^1)),color(black)(Fm),(color(black)([Rn] 7s^2 5f^12))),(color(red)(Np),(color(red)([Rn] 7s^2 5f^4 6d^1)),color(black)(Md),(color(black)([Rn] 7s^2 5f^13))),(color(black)(Pu),(color(black)([Rn] 7s^2 5f^6)),color(black)(No),(color(black)([Rn] 7s^2 5f^14))),(color(black)(Am),(color(black)([Rn] 7s^2 5f^7)),color(black)(Lr),(color(black)([Rn] 7s^2 5f^14 6d^1))),(color(red)(Cm),(color(red)([Rn] 7s^2 5f^7 6d^1)),"","")])#

I cover those in detail here.